141 lines
4.6 KiB
Markdown
141 lines
4.6 KiB
Markdown
# Results
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## Compatibility test
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Comparing sample properties:
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$$
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p = 1 - \text{erf} \left( \frac{t}{\sqrt{2}} \right)\ \with
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t = \frac{|x\ex - x\ob|}{\sqrt{\sigma\ex^2 + \sigma\ob^2}}
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$$
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- $x\ex$ and $x\ob$ are the expected and observed values
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- $\sigma\ex$ and $\sigma\ob$ are their absolute errors
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. . .
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At 95% confidence level, the values are compatible if:
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$$
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p > 0.05
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$$
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## Compatibility test
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\setbeamercovered{}
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\begin{center}
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\begin{tikzpicture}[>=Stealth]
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%notes
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\draw [very thick, gray] (0,0) -- (0,3);
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\draw [very thick, gray] (-1.45,1.5) -- (1.45,1.5);
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\draw [very thick, gray] (-1.35,1.3) -- (-1.55,1.7);
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\draw [very thick, gray] ( 1.35,1.3) -- ( 1.55,1.7);
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\node at (0,-0.4) {$x\ex$};
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\node [right] at (1.7,1.7) {$2 \, \sqrt{\sigma\ex^2 + \sigma\ob^2}$};
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% axes
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\draw [very thick, <->] (-5,4) -- (-5,0) -- (5,0);
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\node [right] at (5,0) {$x$};
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% Gaussian
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\draw [domain=-5:5, smooth, variable=\x, cyclamen, very thick]
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plot ({\x}, {3*exp(-(\x*\x/3))});
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\pause
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% area
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\fill [domain=2:5, smooth, variable=\x, cyclamen!20!white, very thick]
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(2,0) -- plot ({\x}, {3*exp(-(\x*\x/3))}) -- (5,0) -- cycle;
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\fill [domain=-5:-2, smooth, variable=\x, cyclamen!20!white, very thick]
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(-5,0) -- plot ({\x}, {3*exp(-(\x*\x/3))}) -- (-2,0) -- cycle;
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% axes
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\draw [very thick, <->] (-5,4) -- (-5,0) -- (5,0);
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% Gaussian
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\draw [domain=-5:5, smooth, variable=\x, cyclamen, very thick]
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plot ({\x}, {3*exp(-(\x*\x/3))});
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%notes
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\draw [thick, cyclamen] (-2,0) -- (-2,0.8);
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\draw [thick, cyclamen] ( 2,0) -- ( 2,0.8);
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\node at (2,-0.4) {$x\ob$};
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\end{tikzpicture}
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\end{center}
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\setbeamercovered{transparent}
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## L sample results
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\begin{center}
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\begin{tabular}{rcccc}
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\toprule
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& & median & mode & fwhm \\
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\midrule
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\multirow{2}{*}{50000} & $t$ & 0.761 & 1.012 & 1.338 \\
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& $p$ & \gre{0.446} & \gre{0.311} & \gre{0.181} \\
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\midrule
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\multirow{2}{*}{1000} & $t$ & 1.549 & 0.072 & 3.790 \\
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& $p$ & \gre{0.121} & \gre{0.943} & \red{0.000} \\
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\midrule
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\multirow{2}{*}{200} & $t$ & 2.508 & 0.418 & 1.547 \\
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& $p$ & \red{0.012} & \gre{0.676} & \gre{0.122} \\
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\toprule
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\end{tabular}
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\end{center}
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## M sample results
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\begin{center}
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\begin{tabular}{rcccc}
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\toprule
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& & median & mode & fwhm \\
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\midrule
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\multirow{2}{*}{50000} & $t$ & 669.9 & 0.732 & 1.329 \\
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& $p$ & \gre{0.000} & \gre{0.464} & \gre{0.184} \\
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\midrule
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\multirow{2}{*}{1000} & $t$ & 25.47 & 0.665 & 1.890 \\
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& $p$ & \gre{0.000} & \gre{0.506} & \gre{0.059} \\
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\midrule
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\multirow{2}{*}{200} & $t$ & 48.12 & 0.028 & 0.388 \\
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& $p$ & \gre{0.000} & \gre{0.978} & \gre{0.698} \\
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\toprule
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\end{tabular}
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\end{center}
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## KS samples results
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\begin{center}
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\begin{tabular}{rlll}
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\toprule
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& & L sample & M sample \\
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\midrule
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\multirow{2}{*}{50000} & $D$ & 0.004 & 0.153 \\
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& $p$ & \gre{0.379} & \gre{0.000} \\
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\midrule
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\multirow{2}{*}{1000} & $D$ & 0.020 & 0.162 \\
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& $p$ & \gre{0.794} & \gre{0.000} \\
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\midrule
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\multirow{2}{*}{200} & $D$ & 0.086 & 0.226 \\
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& $p$ & \gre{0.100} & \gre{0.000} \\
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\toprule
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\end{tabular}
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\end{center}
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## Trapani samples results
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\begin{center}
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\begin{tabular}{rlllll}
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\toprule
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& & \multicolumn{2}{c}{L sample} & \multicolumn{2}{c}{M sample} \\
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& & mean & variance & mean & variance \\
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\midrule
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\multirow{2}{*}{50000} & $\Theta$ & 0.255 & 0.432 & 161.1 & 162.5 \\
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& $p$ & \gre{0.614} & \gre{0.511} & \gre{0.000} & \gre{0.000} \\
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\midrule
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\multirow{2}{*}{1000} & $\Theta$ & 0.809 & 0.809 & 10.83 & 5.823 \\
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& $p$ & \gre{0.368} & \gre{0.368} & \gre{0.016} & \gre{0.001} \\
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\midrule
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\multirow{2}{*}{200} & $\Theta$ & 0.472 & 0.170 & 2.232 & 2.981 \\
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& $p$ & \gre{0.492} & \gre{0.680} & \red{0.135} & \red{0.084} \\
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\toprule
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\end{tabular}
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\end{center}
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